source("dados_regular.R")
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########## Regressão linear ########
######backward regression #######
#Selecão das variáveis para compor o modelo, mas precisa depois fazer os teste de resÃduo
modelo_back <- lm(WINP ~ PTS + FGP + PF + PlusMinus, data = dados_regressao)
modelo_back
##
## Call:
## lm(formula = WINP ~ PTS + FGP + PF + PlusMinus, data = dados_regressao)
##
## Coefficients:
## (Intercept) PTS FGP PF PlusMinus
## 0.4105976 -0.0006542 0.0048736 -0.0032414 0.0304204
coef(modelo_back)
## (Intercept) PTS FGP PF PlusMinus
## 0.4105975914 -0.0006542452 0.0048736395 -0.0032414270 0.0304203770
anova(modelo_back)
## Analysis of Variance Table
##
## Response: WINP
## Df Sum Sq Mean Sq F value Pr(>F)
## PTS 1 0.9761 0.9761 655.61 < 2.2e-16 ***
## FGP 1 2.8026 2.8026 1882.29 < 2.2e-16 ***
## PF 1 0.2162 0.2162 145.18 < 2.2e-16 ***
## PlusMinus 1 5.5307 5.5307 3714.59 < 2.2e-16 ***
## Residuals 445 0.6626 0.0015
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(modelo_back) #Adjusted R-squared: 0.9344
##
## Call:
## lm(formula = WINP ~ PTS + FGP + PF + PlusMinus, data = dados_regressao)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.113561 -0.026335 0.002916 0.025377 0.130296
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4105976 0.0715538 5.738 1.77e-08 ***
## PTS -0.0006542 0.0003239 -2.020 0.04402 *
## FGP 0.0048736 0.0016969 2.872 0.00427 **
## PF -0.0032414 0.0013132 -2.468 0.01395 *
## PlusMinus 0.0304204 0.0004991 60.947 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03859 on 445 degrees of freedom
## Multiple R-squared: 0.935, Adjusted R-squared: 0.9344
## F-statistic: 1599 on 4 and 445 DF, p-value: < 2.2e-16
AIC(modelo_back) #-1645.353
## [1] -1645.353
###ResÃduos ###
plot(modelo_back, which = 1)
plot(modelo_back, which = 2)
plot(modelo_back, which = 3)
plot(modelo_back, which = 4)
plot(modelo_back, which = 5)
plot(modelo_back, which = 6)
shapiro.test(modelo_back$residuals) #p-value = 0.2669, normal
##
## Shapiro-Wilk normality test
##
## data: modelo_back$residuals
## W = 0.99576, p-value = 0.2669
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_back) #p-value = 0.1735
##
## Durbin-Watson test
##
## data: modelo_back
## DW = 1.9193, p-value = 0.1735
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_back$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_back$fitted.values, modelo_back$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_back) #p-value = 0.0006407, heterocedasticidade
##
## studentized Breusch-Pagan test
##
## data: modelo_back
## BP = 19.451, df = 4, p-value = 0.0006407
#QQ Plot
library(hnp)
## Loading required package: MASS
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hnp(modelo_back)
## Gaussian model (lm object)
######## Forward Selection ########
modelo_forw <- lm(formula = WINP ~ PlusMinus + PF + FGP + FGM, data = dados_regressao)
modelo_forw
##
## Call:
## lm(formula = WINP ~ PlusMinus + PF + FGP + FGM, data = dados_regressao)
##
## Coefficients:
## (Intercept) PlusMinus PF FGP FGM
## 0.401565 0.030261 -0.003478 0.005746 -0.002433
coef(modelo_forw)
## (Intercept) PlusMinus PF FGP FGM
## 0.401564997 0.030260547 -0.003477604 0.005745605 -0.002433190
anova(modelo_forw)
## Analysis of Variance Table
##
## Response: WINP
## Df Sum Sq Mean Sq F value Pr(>F)
## PlusMinus 1 9.5032 9.5032 6398.0581 < 2e-16 ***
## PF 1 0.0096 0.0096 6.4381 0.01151 *
## FGP 1 0.0068 0.0068 4.5541 0.03339 *
## FGM 1 0.0077 0.0077 5.1648 0.02353 *
## Residuals 445 0.6610 0.0015
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(modelo_forw) #Adjusted R-squared: 0.9345
##
## Call:
## lm(formula = WINP ~ PlusMinus + PF + FGP + FGM, data = dados_regressao)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.113414 -0.024898 0.002528 0.025502 0.129168
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4015650 0.0718776 5.587 4.04e-08 ***
## PlusMinus 0.0302605 0.0005057 59.834 < 2e-16 ***
## PF -0.0034776 0.0013110 -2.653 0.00827 **
## FGP 0.0057456 0.0018603 3.089 0.00214 **
## FGM -0.0024332 0.0010707 -2.273 0.02353 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03854 on 445 degrees of freedom
## Multiple R-squared: 0.9351, Adjusted R-squared: 0.9345
## F-statistic: 1604 on 4 and 445 DF, p-value: < 2.2e-16
### ResÃduos ###
plot(modelo_forw, which = 1)
plot(modelo_forw, which = 2) #QQ-plot
plot(modelo_forw, which = 3)
plot(modelo_forw, which = 4)
plot(modelo_forw, which = 5)
plot(modelo_forw, which = 6)
shapiro.test(modelo_forw$residuals) #p-value = 0.2296, não normal
##
## Shapiro-Wilk normality test
##
## data: modelo_forw$residuals
## W = 0.99555, p-value = 0.2296
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_forw) #p-value = 0.195
##
## Durbin-Watson test
##
## data: modelo_forw
## DW = 1.9266, p-value = 0.195
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_forw$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_forw$fitted.values, modelo_forw$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_forw) #p-value = 0.001575, heterocedasticidade
##
## studentized Breusch-Pagan test
##
## data: modelo_forw
## BP = 17.457, df = 4, p-value = 0.001575
library(hnp)
hnp(modelo_forw)
## Gaussian model (lm object)
########## Regressão beta ########
######## Logito ##########
#Melhor modelo logito é o modelo com `3PP` + PF + PlusMinus que é modelo_beta12_3.
modelo_beta12_3 <- betareg(WINP ~ `3PP` + PF + PlusMinus, data = dados_regressao)
modelo_beta12_3
##
## Call:
## betareg(formula = WINP ~ `3PP` + PF + PlusMinus, data = dados_regressao)
##
## Coefficients (mean model with logit link):
## (Intercept) `3PP` PF PlusMinus
## -0.065925 0.009085 -0.013016 0.132901
##
## Phi coefficients (precision model with identity link):
## (phi)
## 157.3
summary(modelo_beta12_3) #Pseudo R-squared: 0.9351
##
## Call:
## betareg(formula = WINP ~ `3PP` + PF + PlusMinus, data = dados_regressao)
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -3.0205 -0.6019 0.0688 0.6351 2.9791
##
## Coefficients (mean model with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.065925 0.215170 -0.306 0.7593
## `3PP` 0.009085 0.005205 1.746 0.0809 .
## PF -0.013016 0.005661 -2.299 0.0215 *
## PlusMinus 0.132901 0.002136 62.218 <2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 157.29 10.46 15.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 834.7 on 5 Df
## Pseudo R-squared: 0.9318
## Number of iterations: 12 (BFGS) + 2 (Fisher scoring)
coef(modelo_beta12_3)
## (Intercept) `3PP` PF PlusMinus (phi)
## -0.065924629 0.009085456 -0.013016005 0.132901031 157.292447304
car::Anova(modelo_beta12_3)
## Analysis of Deviance Table (Type II tests)
##
## Response: WINP
## Df Chisq Pr(>Chisq)
## `3PP` 1 3.0470 0.08089 .
## PF 1 5.2864 0.02149 *
## PlusMinus 1 3871.0668 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
########ResÃduos Logito ###
plot(modelo_beta12_3, which = 1, type = "pearson")
plot(modelo_beta12_3, which = 2, type = "pearson")
plot(modelo_beta12_3, which = 3, type = "pearson")
plot(modelo_beta12_3, which = 4, type = "pearson")
plot(modelo_beta12_3, which = 5, type = "deviance", sub.caption = "")
plot(modelo_beta12_3, which = 1, type = "deviance", sub.caption = "")
shapiro.test(modelo_beta12_3$residuals) #p-value = 0.5895, normal
##
## Shapiro-Wilk normality test
##
## data: modelo_beta12_3$residuals
## W = 0.99475, p-value = 0.1284
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_beta12_3) #p-value = 0.2889
##
## Durbin-Watson test
##
## data: modelo_beta12_3
## DW = 1.936, p-value = 0.2336
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_beta12_3$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_beta12_3$fitted.values, modelo_beta12_3$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_beta12_3) #p-value = 0.03674, heterocedasticidade
##
## studentized Breusch-Pagan test
##
## data: modelo_beta12_3
## BP = 14.444, df = 3, p-value = 0.002359
######## Loglog ##########
#Melhor modelo de loglog é o modelo modelo_beta21 com STL + PF + PlusMinus;
modelo_beta21 <- betareg(WINP ~ STL + PF + PlusMinus,data = dados_regressao, link = "loglog") #Regressão com todos os dados do modelo
modelo_beta21
##
## Call:
## betareg(formula = WINP ~ STL + PF + PlusMinus, data = dados_regressao,
## link = "loglog")
##
## Coefficients (mean model with loglog link):
## (Intercept) STL PF PlusMinus
## 0.596869 0.004795 -0.011997 0.092285
##
## Phi coefficients (precision model with identity link):
## (phi)
## 139.4
summary(modelo_beta21) #Pseudo R-squared: 0.9229
##
## Call:
## betareg(formula = WINP ~ STL + PF + PlusMinus, data = dados_regressao,
## link = "loglog")
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -3.0613 -0.5808 0.0294 0.6645 4.0164
##
## Coefficients (mean model with loglog link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.596869 0.091508 6.523 6.91e-11 ***
## STL 0.004795 0.007444 0.644 0.51949
## PF -0.011997 0.004281 -2.802 0.00508 **
## PlusMinus 0.092285 0.001316 70.130 < 2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 139.407 9.263 15.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 807.6 on 5 Df
## Pseudo R-squared: 0.9229
## Number of iterations: 28 (BFGS) + 2 (Fisher scoring)
coef(modelo_beta21)
## (Intercept) STL PF PlusMinus (phi)
## 0.596868894 0.004794876 -0.011997188 0.092284526 139.407335668
car::Anova(modelo_beta21)
## Analysis of Deviance Table (Type II tests)
##
## Response: WINP
## Df Chisq Pr(>Chisq)
## STL 1 0.4149 0.519487
## PF 1 7.8518 0.005077 **
## PlusMinus 1 4918.2225 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#### ResÃduos loglog ##
plot(modelo_beta21, which = 1, type = "pearson")
plot(modelo_beta21, which = 2, type = "pearson")
plot(modelo_beta21, which = 3, type = "pearson")
plot(modelo_beta21, which = 4, type = "pearson")
plot(modelo_beta21, which = 5, type = "deviance", sub.caption = "")
plot(modelo_beta21, which = 1, type = "deviance", sub.caption = "")
shapiro.test(modelo_beta21$residuals) #p-value =
##
## Shapiro-Wilk normality test
##
## data: modelo_beta21$residuals
## W = 0.99573, p-value = 0.2618
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_beta21) #p-value =
##
## Durbin-Watson test
##
## data: modelo_beta21
## DW = 1.9408, p-value = 0.2497
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_beta21$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_beta21$fitted.values, modelo_beta21$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_beta21) #p-value =
##
## studentized Breusch-Pagan test
##
## data: modelo_beta21
## BP = 15.604, df = 3, p-value = 0.001367
######## Probito ##########
#Melhor modelo de probito é modelo_beta_probit2 com `3PP` + TOV + STL + PF + PlusMinus;
modelo_beta_probit2 <- betareg(WINP ~ `3PP` + TOV + STL + PF + PlusMinus,data = dados_regressao, link = "probit")
modelo_beta_probit2
##
## Call:
## betareg(formula = WINP ~ `3PP` + TOV + STL + PF + PlusMinus, data = dados_regressao,
## link = "probit")
##
## Coefficients (mean model with probit link):
## (Intercept) `3PP` TOV STL PF PlusMinus
## -0.0671991 0.0059479 0.0002532 0.0039662 -0.0089563 0.0816533
##
## Phi coefficients (precision model with identity link):
## (phi)
## 156.5
summary(modelo_beta_probit2) #Pseudo R-squared: 0.9331
##
## Call:
## betareg(formula = WINP ~ `3PP` + TOV + STL + PF + PlusMinus, data = dados_regressao,
## link = "probit")
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -3.0562 -0.6143 0.0566 0.6671 3.0617
##
## Coefficients (mean model with probit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.0671991 0.1501123 -0.448 0.6544
## `3PP` 0.0059479 0.0032840 1.811 0.0701 .
## TOV 0.0002532 0.0049740 0.051 0.9594
## STL 0.0039662 0.0062975 0.630 0.5288
## PF -0.0089563 0.0037562 -2.384 0.0171 *
## PlusMinus 0.0816533 0.0013798 59.178 <2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 156.55 10.41 15.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 833.6 on 7 Df
## Pseudo R-squared: 0.9331
## Number of iterations: 16 (BFGS) + 2 (Fisher scoring)
coef(modelo_beta_probit2)
## (Intercept) `3PP` TOV STL PF
## -6.719908e-02 5.947906e-03 2.532476e-04 3.966216e-03 -8.956325e-03
## PlusMinus (phi)
## 8.165333e-02 1.565477e+02
car::Anova(modelo_beta_probit2)
## Analysis of Deviance Table (Type II tests)
##
## Response: WINP
## Df Chisq Pr(>Chisq)
## `3PP` 1 3.2804 0.07011 .
## TOV 1 0.0026 0.95939
## STL 1 0.3967 0.52882
## PF 1 5.6855 0.01711 *
## PlusMinus 1 3501.9850 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
### ResÃduos Probito ###
plot(modelo_beta_probit2, which = 1, type = "pearson")
plot(modelo_beta_probit2, which = 2, type = "pearson")
plot(modelo_beta_probit2, which = 3, type = "pearson")
plot(modelo_beta_probit2, which = 4, type = "pearson")
plot(modelo_beta_probit2, which = 5, type = "deviance", sub.caption = "")
plot(modelo_beta_probit2, which = 1, type = "deviance", sub.caption = "")
shapiro.test(modelo_beta_probit2$residuals) #p-value =
##
## Shapiro-Wilk normality test
##
## data: modelo_beta_probit2$residuals
## W = 0.99481, p-value = 0.1343
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_beta_probit2) #p-value =
##
## Durbin-Watson test
##
## data: modelo_beta_probit2
## DW = 1.9345, p-value = 0.2271
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_beta_probit2$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_beta_probit2$fitted.values, modelo_beta_probit2$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_beta_probit2) #p-value =
##
## studentized Breusch-Pagan test
##
## data: modelo_beta_probit2
## BP = 16.05, df = 5, p-value = 0.006702
######## cloglog ##########
#melhor modelo é modelo_beta_cloglog_1 com TOV + PlusMinus
modelo_beta_cloglog_1 <- betareg(WINP ~ TOV + PlusMinus,data = dados_regressao, link = "cloglog")
modelo_beta_cloglog_1
##
## Call:
## betareg(formula = WINP ~ TOV + PlusMinus, data = dados_regressao, link = "cloglog")
##
## Coefficients (mean model with cloglog link):
## (Intercept) TOV PlusMinus
## -0.25436 -0.01003 0.09576
##
## Phi coefficients (precision model with identity link):
## (phi)
## 145.3
summary(modelo_beta_cloglog_1) #Pseudo R-squared: 0.9286
##
## Call:
## betareg(formula = WINP ~ TOV + PlusMinus, data = dados_regressao, link = "cloglog")
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -3.4529 -0.6312 0.0437 0.6660 2.4878
##
## Coefficients (mean model with cloglog link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.254364 0.077923 -3.264 0.0011 **
## TOV -0.010035 0.005468 -1.835 0.0665 .
## PlusMinus 0.095761 0.001350 70.951 <2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 145.329 9.658 15.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 817 on 4 Df
## Pseudo R-squared: 0.9249
## Number of iterations: 18 (BFGS) + 2 (Fisher scoring)
coef(modelo_beta_cloglog_1)
## (Intercept) TOV PlusMinus (phi)
## -0.25436364 -0.01003488 0.09576090 145.32881961
car::Anova(modelo_beta_cloglog_1)
## Analysis of Deviance Table (Type II tests)
##
## Response: WINP
## Df Chisq Pr(>Chisq)
## TOV 1 3.3684 0.06646 .
## PlusMinus 1 5034.0170 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#ResÃduos cloglog
plot(modelo_beta_cloglog_1, which = 1, type = "pearson")
plot(modelo_beta_cloglog_1, which = 2, type = "pearson")
plot(modelo_beta_cloglog_1, which = 3, type = "pearson")
plot(modelo_beta_cloglog_1, which = 4, type = "pearson")
plot(modelo_beta_cloglog_1, which = 5, type = "deviance", sub.caption = "")
plot(modelo_beta_cloglog_1, which = 1, type = "deviance", sub.caption = "")
shapiro.test(modelo_beta_cloglog_1$residuals) #p-value =
##
## Shapiro-Wilk normality test
##
## data: modelo_beta_cloglog_1$residuals
## W = 0.99436, p-value = 0.09578
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_beta_cloglog_1) #p-value =
##
## Durbin-Watson test
##
## data: modelo_beta_cloglog_1
## DW = 1.9363, p-value = 0.2385
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_beta_cloglog_1$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_beta_cloglog_1$fitted.values, modelo_beta_cloglog_1$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_beta_cloglog_1) #p-value =
##
## studentized Breusch-Pagan test
##
## data: modelo_beta_cloglog_1
## BP = 4.4453, df = 2, p-value = 0.1083
######## cauchito ##########
modelo_beta_cauchit1 <- betareg(WINP ~ PlusMinus,data = dados_regressao, link = "cauchit")
modelo_beta_cauchit1
##
## Call:
## betareg(formula = WINP ~ PlusMinus, data = dados_regressao, link = "cauchit")
##
## Coefficients (mean model with cauchit link):
## (Intercept) PlusMinus
## -0.008704 0.117730
##
## Phi coefficients (precision model with identity link):
## (phi)
## 153.3
summary(modelo_beta_cauchit1) #Pseudo R-squared: 0.8985
##
## Call:
## betareg(formula = WINP ~ PlusMinus, data = dados_regressao, link = "cauchit")
##
## Standardized weighted residuals 2:
## Min 1Q Median 3Q Max
## -3.5614 -0.6544 0.0255 0.6347 3.9100
##
## Coefficients (mean model with cauchit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.008704 0.006924 -1.257 0.209
## PlusMinus 0.117730 0.001876 62.749 <2e-16 ***
##
## Phi coefficients (precision model with identity link):
## Estimate Std. Error z value Pr(>|z|)
## (phi) 153.27 10.19 15.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 829.1 on 3 Df
## Pseudo R-squared: 0.8985
## Number of iterations: 28 (BFGS) + 2 (Fisher scoring)
coef(modelo_beta_cauchit1)
## (Intercept) PlusMinus (phi)
## -0.008704143 0.117730476 153.265171178
car::Anova(modelo_beta_cauchit1)
## Analysis of Deviance Table (Type II tests)
##
## Response: WINP
## Df Chisq Pr(>Chisq)
## PlusMinus 1 3937.4 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#ResÃduos
plot(modelo_beta_cauchit1, which = 1, type = "pearson")
plot(modelo_beta_cauchit1, which = 2, type = "pearson")
plot(modelo_beta_cauchit1, which = 3, type = "pearson")
plot(modelo_beta_cauchit1, which = 4, type = "pearson")
plot(modelo_beta_cauchit1, which = 5, type = "deviance", sub.caption = "")
plot(modelo_beta_cauchit1, which = 1, type = "deviance", sub.caption = "")
shapiro.test(modelo_beta_cauchit1$residuals) #p-value =
##
## Shapiro-Wilk normality test
##
## data: modelo_beta_cauchit1$residuals
## W = 0.9963, p-value = 0.3833
#Teste de durbin watson para independencia
library(lmtest)
dwtest(modelo_beta_cauchit1) #p-value =
##
## Durbin-Watson test
##
## data: modelo_beta_cauchit1
## DW = 1.9507, p-value = 0.2889
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(modelo_beta_cauchit1$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Homocedasticidade
plot(modelo_beta_cauchit1$fitted.values, modelo_beta_cauchit1$residuals,
xlab = "Valores Ajustados",
ylab = "Residuos",
pch = 19,
main = "Suposição de homocedasticidade"
)
#Breusch_Pagan para homocedasticdade
bptest(modelo_beta_cauchit1) #p-value =
##
## studentized Breusch-Pagan test
##
## data: modelo_beta_cauchit1
## BP = 4.3624, df = 1, p-value = 0.03674
########## GAMLSS ########
######## Forward Beta ##########
gamlss_beta_forw = gamlss(formula = WINP ~ PlusMinus + FGP + PTS + PF, family = BE, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1321.858
## GAMLSS-RS iteration 2: Global Deviance = -1676.336
## GAMLSS-RS iteration 3: Global Deviance = -1676.843
## GAMLSS-RS iteration 4: Global Deviance = -1676.843
gamlss_beta_forw
##
## Family: c("BE", "Beta")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ PlusMinus + FGP + PTS + PF,
## family = BE, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) PlusMinus FGP PTS PF
## -0.505065 0.131669 0.023267 -0.003065 -0.012155
## Sigma Coefficients:
## (Intercept)
## -2.458
##
## Degrees of Freedom for the fit: 6 Residual Deg. of Freedom 444
## Global Deviance: -1676.84
## AIC: -1664.84
## SBC: -1640.19
coef(gamlss_beta_forw)
## (Intercept) PlusMinus FGP PTS PF
## -0.505064513 0.131668749 0.023266609 -0.003064737 -0.012154978
summary(gamlss_beta_forw) #AIC: -1664.843
## ******************************************************************
## Family: c("BE", "Beta")
##
## Call: gamlss(formula = WINP ~ PlusMinus + FGP + PTS + PF,
## family = BE, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: logit
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.505065 0.305547 -1.653 0.09904 .
## PlusMinus 0.131669 0.002219 59.330 < 2e-16 ***
## FGP 0.023267 0.007249 3.210 0.00143 **
## PTS -0.003065 0.001395 -2.198 0.02849 *
## PF -0.012155 0.005639 -2.156 0.03165 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: logit
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.45847 0.03586 -68.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 6
## Residual Deg. of Freedom: 444
## at cycle: 4
##
## Global Deviance: -1676.843
## AIC: -1664.843
## SBC: -1640.188
## ******************************************************************
##### ResÃduos ###
plot(gamlss_beta_forw)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.003493076
## variance = 1.002508
## coef. of skewness = -0.1366816
## coef. of kurtosis = 3.200036
## Filliben correlation coefficient = 0.9980074
## ******************************************************************
shapiro.test(gamlss_beta_forw$residuals) #p-value = 0.2853, normal
##
## Shapiro-Wilk normality test
##
## data: gamlss_beta_forw$residuals
## W = 0.99586, p-value = 0.2853
#Teste de durbin watson para independencia
library(lmtest)
dwtest(gamlss_beta_forw) #p-value = 0.1735
##
## Durbin-Watson test
##
## data: gamlss_beta_forw
## DW = 1.9193, p-value = 0.1735
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(gamlss_beta_forw$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(gamlss_beta_forw) #p-value = 0.0006407
##
## studentized Breusch-Pagan test
##
## data: gamlss_beta_forw
## BP = 19.451, df = 4, p-value = 0.0006407
######## Forward Normal ##########
#Mesma que a linear então não iremos utilizar
gamlss_normal_forw <- gamlss(formula = WINP ~ PlusMinus + PF + FGP + FGM, family = NO, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1658.44
## GAMLSS-RS iteration 2: Global Deviance = -1658.44
gamlss_normal_forw
##
## Family: c("NO", "Normal")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ PlusMinus + PF + FGP + FGM,
## family = NO, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) PlusMinus PF FGP FGM
## 0.401565 0.030261 -0.003478 0.005746 -0.002433
## Sigma Coefficients:
## (Intercept)
## -3.262
##
## Degrees of Freedom for the fit: 6 Residual Deg. of Freedom 444
## Global Deviance: -1658.44
## AIC: -1646.44
## SBC: -1621.78
coef(gamlss_normal_forw)
## (Intercept) PlusMinus PF FGP FGM
## 0.401564997 0.030260547 -0.003477604 0.005745605 -0.002433190
summary(gamlss_normal_forw) #-1646.44
## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = WINP ~ PlusMinus + PF + FGP + FGM,
## family = NO, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4015650 0.0714772 5.618 3.41e-08 ***
## PlusMinus 0.0302605 0.0005029 60.170 < 2e-16 ***
## PF -0.0034776 0.0013037 -2.667 0.00792 **
## FGP 0.0057456 0.0018499 3.106 0.00202 **
## FGM -0.0024332 0.0010647 -2.285 0.02276 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.26165 0.03333 -97.85 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 6
## Residual Deg. of Freedom: 444
## at cycle: 2
##
## Global Deviance: -1658.44
## AIC: -1646.44
## SBC: -1621.784
## ******************************************************************
#ResÃduos forw
plot(gamlss_normal_forw)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -5.234287e-19
## variance = 1.002227
## coef. of skewness = -0.1543876
## coef. of kurtosis = 3.054637
## Filliben correlation coefficient = 0.9977486
## ******************************************************************
shapiro.test(gamlss_normal_forw$residuals) #p-value = 0.2296, normal
##
## Shapiro-Wilk normality test
##
## data: gamlss_normal_forw$residuals
## W = 0.99555, p-value = 0.2296
#Teste de durbin watson para independencia
library(lmtest)
dwtest(gamlss_normal_forw) #p-value = 0.195
##
## Durbin-Watson test
##
## data: gamlss_normal_forw
## DW = 1.9266, p-value = 0.195
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(gamlss_normal_forw$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(gamlss_normal_forw) #p-value = 0.001575
##
## studentized Breusch-Pagan test
##
## data: gamlss_normal_forw
## BP = 17.457, df = 4, p-value = 0.001575
######## Backward Normal ##########
#Mesma que a linear então não iremos utilizar
gamlss_normal_back <- gamlss(formula = WINP ~ PTS + FGP + PF + PlusMinus, family = NO, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1657.353
## GAMLSS-RS iteration 2: Global Deviance = -1657.353
gamlss_normal_back
##
## Family: c("NO", "Normal")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ PTS + FGP + PF + PlusMinus,
## family = NO, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) PTS FGP PF PlusMinus
## 0.4105976 -0.0006542 0.0048736 -0.0032414 0.0304204
## Sigma Coefficients:
## (Intercept)
## -3.26
##
## Degrees of Freedom for the fit: 6 Residual Deg. of Freedom 444
## Global Deviance: -1657.35
## AIC: -1645.35
## SBC: -1620.7
coef(gamlss_normal_back)
## (Intercept) PTS FGP PF PlusMinus
## 0.4105975914 -0.0006542452 0.0048736395 -0.0032414270 0.0304203770
summary(gamlss_normal_back) #AIC: -1645.353
## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = WINP ~ PTS + FGP + PF + PlusMinus,
## family = NO, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4105976 0.0711551 5.770 1.49e-08 ***
## PTS -0.0006542 0.0003221 -2.031 0.04285 *
## FGP 0.0048736 0.0016875 2.888 0.00406 **
## PF -0.0032414 0.0013059 -2.482 0.01343 *
## PlusMinus 0.0304204 0.0004963 61.289 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.26044 0.03333 -97.81 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 6
## Residual Deg. of Freedom: 444
## at cycle: 2
##
## Global Deviance: -1657.353
## AIC: -1645.353
## SBC: -1620.698
## ******************************************************************
#ResÃduos
plot(gamlss_normal_back)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -6.457791e-17
## variance = 1.002227
## coef. of skewness = -0.1456677
## coef. of kurtosis = 3.071416
## Filliben correlation coefficient = 0.9978431
## ******************************************************************
shapiro.test(gamlss_normal_back$residuals) #p-value = 0.2669, normal
##
## Shapiro-Wilk normality test
##
## data: gamlss_normal_back$residuals
## W = 0.99576, p-value = 0.2669
#Teste de durbin watson para independencia
library(lmtest)
dwtest(gamlss_normal_back) #p-value = 0.1735
##
## Durbin-Watson test
##
## data: gamlss_normal_back
## DW = 1.9193, p-value = 0.1735
## alternative hypothesis: true autocorrelation is greater than 0
#Independência
plot(gamlss_normal_back$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(gamlss_normal_back) #p-value = 0.0006407
##
## studentized Breusch-Pagan test
##
## data: gamlss_normal_back
## BP = 19.451, df = 4, p-value = 0.0006407
########## Modelos Mistos ########
##### Normal TEAM #####
misto_normal_team <- gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
PlusMinus + OREB + PF + `3PA`, family = NO, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1692.952
## GAMLSS-RS iteration 2: Global Deviance = -1692.953
misto_normal_team
##
## Family: c("NO", "Normal")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
## PlusMinus + OREB + PF + `3PA`, family = NO, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) re(random = ~1 | TEAM) PlusMinus
## 0.6092070 NA 0.0309516
## OREB PF `3PA`
## -0.0039632 -0.0027516 -0.0004534
## Sigma Coefficients:
## (Intercept)
## -3.3
##
## Degrees of Freedom for the fit: 18.68 Residual Deg. of Freedom 431.3
## Global Deviance: -1692.95
## AIC: -1655.59
## SBC: -1578.82
coef(misto_normal_team)
## (Intercept) re(random = ~1 | TEAM) PlusMinus
## 0.609207002 NA 0.030951603
## OREB PF `3PA`
## -0.003963203 -0.002751593 -0.000453441
summary(misto_normal_team) #AIC:
## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
## PlusMinus + OREB + PF + `3PA`, family = NO, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6092070 0.0303785 20.054 <2e-16 ***
## PlusMinus 0.0309516 0.0003838 80.651 <2e-16 ***
## OREB -0.0039632 0.0015319 -2.587 0.0100 *
## PF -0.0027516 0.0012698 -2.167 0.0308 *
## `3PA` -0.0004534 0.0002449 -1.852 0.0648 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.30000 0.03333 -99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## NOTE: Additive smoothing terms exist in the formulas:
## i) Std. Error for smoothers are for the linear effect only.
## ii) Std. Error for the linear terms maybe are not accurate.
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 18.68251
## Residual Deg. of Freedom: 431.3175
## at cycle: 2
##
## Global Deviance: -1692.953
## AIC: -1655.588
## SBC: -1578.817
## ******************************************************************
getSmo(misto_normal_team)
## Linear mixed-effects model fit by maximum likelihood
## Data: Data
## Log-likelihood: 830.6558
## Fixed: fix.formula
## (Intercept)
## -7.716467e-05
##
## Random effects:
## Formula: ~1 | TEAM
## (Intercept) Residual
## StdDev: 0.008588527 1.015556
##
## Variance function:
## Structure: fixed weights
## Formula: ~W.var
## Number of Observations: 450
## Number of Groups: 34
#ResÃduos
plot(misto_normal_team)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 3.759596e-16
## variance = 1.002227
## coef. of skewness = -0.16376
## coef. of kurtosis = 3.164814
## Filliben correlation coefficient = 0.9976843
## ******************************************************************
shapiro.test(misto_normal_team$residuals) #p-value = normal
##
## Shapiro-Wilk normality test
##
## data: misto_normal_team$residuals
## W = 0.99567, p-value = 0.2499
#Independência
plot(misto_normal_team$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(misto_normal_team) #p-value =
##
## studentized Breusch-Pagan test
##
## data: misto_normal_team
## BP = 19.427, df = 4, p-value = 0.0006477
###### Forward Normal Temporada #####
misto_normal_forw_temp <- gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
PlusMinus + PF + FGP + FGM, family = NO, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1658.44
## GAMLSS-RS iteration 2: Global Deviance = -1658.44
misto_normal_forw_temp
##
## Family: c("NO", "Normal")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
## PlusMinus + PF + FGP + FGM, family = NO, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) re(random = ~1 | Numero_temporada)
## 0.401565 NA
## PlusMinus PF
## 0.030261 -0.003478
## FGP FGM
## 0.005746 -0.002433
## Sigma Coefficients:
## (Intercept)
## -3.262
##
## Degrees of Freedom for the fit: 5 Residual Deg. of Freedom 445
## Global Deviance: -1658.44
## AIC: -1648.44
## SBC: -1627.89
coef(misto_normal_forw_temp)
## (Intercept) re(random = ~1 | Numero_temporada)
## 0.401564997 NA
## PlusMinus PF
## 0.030260547 -0.003477604
## FGP FGM
## 0.005745605 -0.002433190
summary(misto_normal_forw_temp) #AIC:
## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
## PlusMinus + PF + FGP + FGM, family = NO, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4015650 0.0714772 5.618 3.41e-08 ***
## PlusMinus 0.0302605 0.0005029 60.170 < 2e-16 ***
## PF -0.0034776 0.0013037 -2.667 0.00792 **
## FGP 0.0057456 0.0018499 3.106 0.00202 **
## FGM -0.0024332 0.0010647 -2.285 0.02276 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.26165 0.03333 -97.85 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## NOTE: Additive smoothing terms exist in the formulas:
## i) Std. Error for smoothers are for the linear effect only.
## ii) Std. Error for the linear terms maybe are not accurate.
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 5
## Residual Deg. of Freedom: 445
## at cycle: 2
##
## Global Deviance: -1658.44
## AIC: -1648.44
## SBC: -1627.894
## ******************************************************************
getSmo(misto_normal_forw_temp)
## Linear mixed-effects model fit by maximum likelihood
## Data: Data
## Log-likelihood: 829.22
## Fixed: fix.formula
## (Intercept)
## -2.406961e-18
##
## Random effects:
## Formula: ~1 | Numero_temporada
## (Intercept) Residual
## StdDev: 2.425336e-07 0.9999995
##
## Variance function:
## Structure: fixed weights
## Formula: ~W.var
## Number of Observations: 450
## Number of Groups: 15
#ResÃduos
plot(misto_normal_forw_temp)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -2.760282e-16
## variance = 1.002227
## coef. of skewness = -0.1543876
## coef. of kurtosis = 3.054637
## Filliben correlation coefficient = 0.9977486
## ******************************************************************
shapiro.test(misto_normal_forw_temp$residuals) #p-value = normal
##
## Shapiro-Wilk normality test
##
## data: misto_normal_forw_temp$residuals
## W = 0.99555, p-value = 0.2296
#Independência
plot(misto_normal_forw_temp$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(misto_normal_forw_temp) #p-value =
##
## studentized Breusch-Pagan test
##
## data: misto_normal_forw_temp
## BP = 17.457, df = 4, p-value = 0.001575
###### Beta Team ####
misto_beta_forw_team <- gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
PlusMinus + FGP + PTS + PF, family = BE, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1331.692
## GAMLSS-RS iteration 2: Global Deviance = -1702.507
## GAMLSS-RS iteration 3: Global Deviance = -1703.008
## GAMLSS-RS iteration 4: Global Deviance = -1702.989
## GAMLSS-RS iteration 5: Global Deviance = -1702.988
misto_beta_forw_team
##
## Family: c("BE", "Beta")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
## PlusMinus + FGP + PTS + PF, family = BE, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) re(random = ~1 | TEAM) PlusMinus
## -0.52046 NA 0.13127
## FGP PTS PF
## 0.02313 -0.00305 -0.01114
## Sigma Coefficients:
## (Intercept)
## -2.49
##
## Degrees of Freedom for the fit: 15.52 Residual Deg. of Freedom 434.5
## Global Deviance: -1702.99
## AIC: -1671.94
## SBC: -1608.14
coef(misto_beta_forw_team)
## (Intercept) re(random = ~1 | TEAM) PlusMinus
## -0.520457363 NA 0.131270482
## FGP PTS PF
## 0.023125273 -0.003050261 -0.011143861
summary(misto_beta_forw_team) #AIC:
## ******************************************************************
## Family: c("BE", "Beta")
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | TEAM)) +
## PlusMinus + FGP + PTS + PF, family = BE, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: logit
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.520457 0.296861 -1.753 0.08027 .
## PlusMinus 0.131270 0.002155 60.912 < 2e-16 ***
## FGP 0.023125 0.007044 3.283 0.00111 **
## PTS -0.003050 0.001355 -2.251 0.02490 *
## PF -0.011144 0.005475 -2.035 0.04243 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: logit
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.48957 0.03579 -69.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## NOTE: Additive smoothing terms exist in the formulas:
## i) Std. Error for smoothers are for the linear effect only.
## ii) Std. Error for the linear terms maybe are not accurate.
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 15.52489
## Residual Deg. of Freedom: 434.4751
## at cycle: 5
##
## Global Deviance: -1702.988
## AIC: -1671.938
## SBC: -1608.143
## ******************************************************************
getSmo(misto_beta_forw_team)
## Linear mixed-effects model fit by maximum likelihood
## Data: Data
## Log-likelihood: 172.8376
## Fixed: fix.formula
## (Intercept)
## -0.000240694
##
## Random effects:
## Formula: ~1 | TEAM
## (Intercept) Residual
## StdDev: 0.03017841 1.011871
##
## Variance function:
## Structure: fixed weights
## Formula: ~W.var
## Number of Observations: 450
## Number of Groups: 34
#ResÃduos
plot(misto_beta_forw_team)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.003213294
## variance = 1.002233
## coef. of skewness = -0.1191569
## coef. of kurtosis = 3.196833
## Filliben correlation coefficient = 0.9981705
## ******************************************************************
shapiro.test(misto_beta_forw_team$residuals) #p-value = normal
##
## Shapiro-Wilk normality test
##
## data: misto_beta_forw_team$residuals
## W = 0.99621, p-value = 0.3609
#Independência
plot(misto_beta_forw_team$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(misto_beta_forw_team) #p-value =
##
## studentized Breusch-Pagan test
##
## data: misto_beta_forw_team
## BP = 19.451, df = 4, p-value = 0.0006407
##### Backward Beta Temporada #####
misto_beta_temp <- gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
PlusMinus + PF + FGP + FGA, family = BE, data = dados_regressao)
## GAMLSS-RS iteration 1: Global Deviance = -1321.864
## GAMLSS-RS iteration 2: Global Deviance = -1676.074
## GAMLSS-RS iteration 3: Global Deviance = -1676.579
## GAMLSS-RS iteration 4: Global Deviance = -1676.579
misto_beta_temp
##
## Family: c("BE", "Beta")
## Fitting method: RS()
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
## PlusMinus + PF + FGP + FGA, family = BE, data = dados_regressao)
##
## Mu Coefficients:
## (Intercept) re(random = ~1 | Numero_temporada)
## -0.144351 NA
## PlusMinus PF
## 0.131028 -0.013171
## FGP FGA
## 0.017272 -0.004551
## Sigma Coefficients:
## (Intercept)
## -2.458
##
## Degrees of Freedom for the fit: 5 Residual Deg. of Freedom 445
## Global Deviance: -1676.58
## AIC: -1666.58
## SBC: -1646.03
coef(misto_beta_temp)
## (Intercept) re(random = ~1 | Numero_temporada)
## -0.144351152 NA
## PlusMinus PF
## 0.131028037 -0.013171238
## FGP FGA
## 0.017272427 -0.004550627
summary(misto_beta_temp) #AIC:
## ******************************************************************
## Family: c("BE", "Beta")
##
## Call: gamlss(formula = WINP ~ (re(random = ~1 | Numero_temporada)) +
## PlusMinus + PF + FGP + FGA, family = BE, data = dados_regressao)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: logit
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.144351 0.330670 -0.437 0.66266
## PlusMinus 0.131028 0.002248 58.298 < 2e-16 ***
## PF -0.013171 0.005636 -2.337 0.01987 *
## FGP 0.017272 0.006264 2.757 0.00607 **
## FGA -0.004551 0.002125 -2.141 0.03280 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: logit
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.45814 0.03586 -68.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## NOTE: Additive smoothing terms exist in the formulas:
## i) Std. Error for smoothers are for the linear effect only.
## ii) Std. Error for the linear terms maybe are not accurate.
## ------------------------------------------------------------------
## No. of observations in the fit: 450
## Degrees of Freedom for the fit: 5
## Residual Deg. of Freedom: 445
## at cycle: 4
##
## Global Deviance: -1676.579
## AIC: -1666.579
## SBC: -1646.033
## ******************************************************************
getSmo(misto_beta_temp)
## Linear mixed-effects model fit by maximum likelihood
## Data: Data
## Log-likelihood: 171.5918
## Fixed: fix.formula
## (Intercept)
## 2.707631e-13
##
## Random effects:
## Formula: ~1 | Numero_temporada
## (Intercept) Residual
## StdDev: 3.331254e-06 0.9997892
##
## Variance function:
## Structure: fixed weights
## Formula: ~W.var
## Number of Observations: 450
## Number of Groups: 15
#ResÃduos
plot(misto_beta_temp)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.003259703
## variance = 1.002493
## coef. of skewness = -0.1504399
## coef. of kurtosis = 3.186479
## Filliben correlation coefficient = 0.9977991
## ******************************************************************
shapiro.test(misto_beta_temp$residuals) #p-value = normal
##
## Shapiro-Wilk normality test
##
## data: misto_beta_temp$residuals
## W = 0.99535, p-value = 0.2
#Independência
plot(misto_beta_temp$residuals,
ylab = "Residuos",
xlab = "Index dos Imovéis",
main = "Suposição de independência",
pch = 19)
#Breusch_Pagan para homocedasticdade
bptest(misto_beta_temp) #p-value =
##
## studentized Breusch-Pagan test
##
## data: misto_beta_temp
## BP = 17.534, df = 4, p-value = 0.001522